In section 1 we investigate the properties of a self-conjugate function on a Boolean algebra (BA). In section 2, the notion of self-conjugacy will then be extended to functions of more than one variable and Boolean algebras with operators in which each of the additional operations has this property will be examined. In particular, we extend the definition of ideal element to every structure of this type. The notation of [3] will be used and a familiarity with that paper is assumed. In addition,/" will represent the composition of / with itself n times and id will denote the identity function on a BA.